Accurate statistical data about medical intervention outcomes are often confusing, incomplete or inaccessible to patients. Without such information, patients are frustrated, and the spirit of informed consent is thwarted. Even when relevant data are available, they may not be correctly communicated. Practicing physicians may not provide accurate counsel about, for example, the probabilistic implications of test results. Consequently, false positive results from medical tests result in needless anxiety, and false negatives result in needless delay. Moreover, some physicians recommend treatments they prefer instead of undertaking the time-consuming effort to make the patient an informed decision maker. Physicians and medical counselors themselves are often confused about the implications of complex numerical information. Poor communication of risks can lead to patients making poor choices. Physicians and their patients will benefit from software tools that answer two needs within the broad field of clinical decision support: (1) helping explain the meaning of the results of a medical test in a way that is understandable and accurate, and (2) helping to decide among treatment options. The relevant information is usually encoded in terms of outcome frequencies or probabilities, but there are two serious complicating issues. The first issue is that there is usually uncertainty about the data arising from sampling error due to limited sample sizes, random measurement error, and a variety of systematic measurement biases. The second complicating issue is that humans are beset by a host of cognitive illusions that confuse their perception of frequency and probability information. Our proposed technology to address these two software needs differs from previous attempts in two main ways. First, we explicitly represent the uncertainty about frequencies and probabilities using robust Bayes methods (also known as Bayesian sensitivity analysis) which are part of the theory of imprecise probabilities. These methods allow us to generate practical advice in the face of uncertainty. For instance, when information is added to an assessment to personalize it for an individual, the uncertainty about a probability might widen if sample sizes are much smaller for subgroups. Second, we make use of findings in psychometry to compensate for cognitive illusions in the perception of frequencies and probabilities. Although statistical innumeracy is often attributed to mental biases and misperceptions, we believe that recent research is convincing that many of the misunderstandings and failures to communicate are caused by flawed presentation of medical statistics. Clinical and other evidence suggest that data formats strongly affect interpretability. Our techniques will compensate for cognitive biases and convey risks in a proper light so that their implications are easily understood. PUBLIC HEALTH RELEVANCE: Statistical data about test results and medical intervention outcomes are often confusing because imprecision about frequencies is hard to convey and because of multiple cognitive illusions about uncertainty. Physicians and their patients will benefit from well designed software tools that compensate for these problems to (1) explain the meaning of the results of a medical test in a way that is understandable and accurate, and (2) help to decide among treatment options that often have complex arrays of probabilistic outcomes.